Motivacija i opis problema

Ličnost je jedna od središnjih tema psihologije, a danas se najčešće opisuje putem petofaktorskog modela Big Five, koji uključuje: ekstraverziju (razlikuje osobe po razini društvene angažiranosti), ugodnost (obuhvaća empatiju i kooperativnost nasuprot sumnjičavosti), savjesnost (govori o odgovornosti nasuprot neorganiziranosti), neuroticizam (opisuje emocionalnu nestabilnost i sklonost negativnim emocijama) te otvorenost (označava kreativnost nasuprot konvencionalnosti). Uz te osnovne dimenzije, česte su i procjene tzv. mračne trijade: narcizma (povišen osjećaj vlastite važnosti i manjak empatije), psihopatije (impulzivnost, bezosjećajnost i antisocijalnost) i makijavelizma (manipulativnost i instrumentalno iskorištavanje drugih). Cilj ovog projekta je analizirati u kakvoj su vezi osnovne crte ličnosti, mračne crte ličnosti te sklonost stresu, depresiji i anksioznosti.

Učitavanje i pregled podataka

Podatke iz CSV datoteke učitavamo u varijablu dataset kako bismo ih mogle bolje analizirati.

dataset <- read_csv('Personality_data.csv')
## New names:
## Rows: 578 Columns: 18
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (5): age, sex, ethnicity simplified, student status, employment status dbl
## (13): ...1, depression, anxiety, stress, narcissism, machiavelism, psych...
## ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
## Specify the column types or set `show_col_types = FALSE` to quiet this message.
## • `` -> `...1`

Dalje, prikažemo prvih nekoliko redaka da vidimo primjere vrijednosti svakog od stupaca.

head(dataset)

Zatim, pomoću metoda names() i glimpse(), dajemo si bolji uvid u tipove podataka i strukturu.

names(dataset)
##  [1] "...1"                 "depression"           "anxiety"             
##  [4] "stress"               "narcissism"           "machiavelism"        
##  [7] "psychoticism"         "sadism"               "neuroticism"         
## [10] "extraversion"         "openness"             "agreeableness"       
## [13] "conscientiousness"    "age"                  "sex"                 
## [16] "ethnicity simplified" "student status"       "employment status"
glimpse(dataset)
## Rows: 578
## Columns: 18
## $ ...1                   <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, …
## $ depression             <dbl> 1.24028239, 1.07356352, -0.58072240, 3.03206310…
## $ anxiety                <dbl> 1.07785482, 1.15519418, -0.26310737, 1.98720356…
## $ stress                 <dbl> 0.50512161, 0.26619388, -0.55579868, 1.94173788…
## $ narcissism             <dbl> 1.50455897, 0.79126351, -0.26693805, 0.41549063…
## $ machiavelism           <dbl> 0.25408691, 0.56182597, -0.69164422, 0.85587890…
## $ psychoticism           <dbl> -0.20141634, 1.31253355, -0.69076562, 2.1866752…
## $ sadism                 <dbl> 0.01933759, 0.86951395, -0.20777818, 1.10452165…
## $ neuroticism            <dbl> -0.20124424, 0.56874269, -0.19237042, 1.4630829…
## $ extraversion           <dbl> 0.64878308, 0.44347482, -1.75862486, -1.8731478…
## $ openness               <dbl> 0.2455288, -0.9359119, -0.6614584, 1.8180786, -…
## $ agreeableness          <dbl> -0.02353314, -1.17591066, -0.31643069, 0.655438…
## $ conscientiousness      <dbl> -0.042944525, -1.043162336, -0.481776915, 0.039…
## $ age                    <chr> "CONSENT_REVOKED", "CONSENT_REVOKED", "29", "37…
## $ sex                    <chr> "CONSENT_REVOKED", "CONSENT_REVOKED", "Female",…
## $ `ethnicity simplified` <chr> "CONSENT_REVOKED", "CONSENT_REVOKED", "Black", …
## $ `student status`       <chr> "CONSENT_REVOKED", "CONSENT_REVOKED", "DATA_EXP…
## $ `employment status`    <chr> "CONSENT_REVOKED", "CONSENT_REVOKED", "DATA_EXP…

Prema uvidu u strukturu podataka vidljivo je da je varijabla age tipa character, što nije prikladno jer bi u statističkim modelima bila tretirana kao kategorijska umjesto numerička varijabla. Stoga je varijabla age pretvorena u numerički tip podataka.

Varijabla sex predstavlja kategorijsku varijablu te je, radi ispravne primjene u regresijskim modelima, pretvorena u tip factor.

Kako bi se osigurala valjanost analize, iz uzorka su uklonjeni svi ispitanici koji sadrže vrijednosti CONSENT_REVOKED ili DATA_EXPIRED, budući da ti zapisi ne predstavljaju stvarne podatke ispitanika.

data_clean <- dataset %>%
  filter(
    if_all(everything(),
           ~ !(. %in% c("CONSENT_REVOKED", "DATA_EXPIRED")))
  ) %>%
  mutate(
    age = as.numeric(age),
    sex = factor(sex)
  )


head(data_clean)

Jesu li ljudi s izraženijom mračnom trijadom skloniji depresiji?

Upoznavanje podataka

describe(data_clean %>%
  select(depression, narcissism, machiavelism, psychoticism))
ggplot(data_clean, aes(narcissism, depression)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

ggplot(data_clean, aes(machiavelism, depression)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

ggplot(data_clean, aes(psychoticism, depression)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

Pearsonove korelacije

cor.test(data_clean$depression, data_clean$narcissism)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$depression and data_clean$narcissism
## t = -4.2976, df = 396, p-value = 2.176e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3031034 -0.1151869
## sample estimates:
##        cor 
## -0.2110948
cor.test(data_clean$depression, data_clean$machiavelism)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$depression and data_clean$machiavelism
## t = 3.1025, df = 396, p-value = 0.002057
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.05660396 0.24857887
## sample estimates:
##       cor 
## 0.1540449
cor.test(data_clean$depression, data_clean$psychoticism)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$depression and data_clean$psychoticism
## t = 4.0662, df = 396, p-value = 5.767e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1039454 0.2927352
## sample estimates:
##       cor 
## 0.2001979
vars1 <- data_clean %>%
  select(depression, narcissism, machiavelism, psychoticism) %>%
  na.omit()

corrplot(cor(vars1))

Linearna regresija

model_dark_triad <- lm(depression ~ narcissism + machiavelism + psychoticism,
             data = data_clean)

summary(model_dark_triad)
## 
## Call:
## lm(formula = depression ~ narcissism + machiavelism + psychoticism, 
##     data = data_clean)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3437 -0.6086 -0.1376  0.5302  3.5540 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.03894    0.05100   0.763 0.445638    
## narcissism   -0.39957    0.05334  -7.490 4.55e-13 ***
## machiavelism  0.20893    0.05434   3.845 0.000141 ***
## psychoticism  0.28178    0.05770   4.884 1.52e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.013 on 394 degrees of freedom
## Multiple R-squared:  0.1648, Adjusted R-squared:  0.1585 
## F-statistic: 25.92 on 3 and 394 DF,  p-value: 2.545e-15
model_all_vars <- lm(depression ~ narcissism + machiavelism + psychoticism +
               neuroticism + extraversion + openness +
               agreeableness + conscientiousness +
               age + sex,
             data = data_clean)

summary(model_all_vars)
## 
## Call:
## lm(formula = depression ~ narcissism + machiavelism + psychoticism + 
##     neuroticism + extraversion + openness + agreeableness + conscientiousness + 
##     age + sex, data = data_clean)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.04151 -0.47610  0.00567  0.48682  3.14221 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.140193   0.307609  -0.456  0.64883    
## narcissism           -0.028672   0.056505  -0.507  0.61214    
## machiavelism          0.042643   0.048557   0.878  0.38038    
## psychoticism          0.147544   0.055444   2.661  0.00811 ** 
## neuroticism           0.456063   0.058382   7.812 5.39e-14 ***
## extraversion         -0.240851   0.061139  -3.939 9.69e-05 ***
## openness              0.041799   0.043854   0.953  0.34111    
## agreeableness         0.042698   0.055370   0.771  0.44110    
## conscientiousness    -0.035091   0.056614  -0.620  0.53574    
## age                   0.002255   0.009454   0.239  0.81160    
## sexMale               0.154454   0.089629   1.723  0.08564 .  
## sexPrefer not to say  0.204176   0.497526   0.410  0.68175    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8454 on 386 degrees of freedom
## Multiple R-squared:  0.4302, Adjusted R-squared:  0.4139 
## F-statistic: 26.49 on 11 and 386 DF,  p-value: < 2.2e-16
vars2 <- data_clean %>%
  select(depression, narcissism, machiavelism, psychoticism,
               neuroticism, extraversion, openness,
               agreeableness, conscientiousness,
               age) %>%
  na.omit()

corrplot(cor(vars2))

data_clean <- data_clean %>%
  mutate(dark_triad = rowMeans(
    select(., narcissism, machiavelism, psychoticism),
    na.rm = TRUE
  ))

cor.test(data_clean$dark_triad, data_clean$depression)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$dark_triad and data_clean$depression
## t = 1.1439, df = 396, p-value = 0.2534
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.04114339  0.15481149
## sample estimates:
##        cor 
## 0.05738674
lm(depression ~ dark_triad + neuroticism + age + sex,
   data = data_clean) |> summary()
## 
## Call:
## lm(formula = depression ~ dark_triad + neuroticism + age + sex, 
##     data = data_clean)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4244 -0.5201  0.0228  0.5018  2.5687 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.304958   0.314088  -0.971   0.3322    
## dark_triad            0.018420   0.054970   0.335   0.7377    
## neuroticism           0.654906   0.041861  15.645   <2e-16 ***
## age                   0.006593   0.009663   0.682   0.4955    
## sexMale               0.192186   0.090412   2.126   0.0342 *  
## sexPrefer not to say  0.155526   0.506531   0.307   0.7590    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8695 on 392 degrees of freedom
## Multiple R-squared:  0.3878, Adjusted R-squared:  0.3799 
## F-statistic: 49.65 on 5 and 392 DF,  p-value: < 2.2e-16

Korelacijska matrica

# odabir 
traits_vars <- dataset %>%
  select(
    depression, anxiety, stress,
    narcissism, machiavelism, psychoticism, sadism,
    neuroticism, extraversion, openness, agreeableness, conscientiousness
  )

# korelacijska matrica
corr_mat <- cor(traits_vars, use = "pairwise.complete.obs")

# korelacijska heatmapa
ggcorrplot(
  corr_mat,
  type = "lower",
  lab = TRUE,
  lab_size = 3,
  hc.order = TRUE,
  outline.col = "white"
)
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## ℹ The deprecated feature was likely used in the ggcorrplot package.
##   Please report the issue at <https://github.com/kassambara/ggcorrplot/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Osobe s većom anksioznošću, depresijom i stresom imaju tendenciju biti i više neurotične.

Mračne osobine su međusobno umjereno povezane.

Visoka savjesnost štiti od depresije i stresa (negativna korelacija).

Ugodnost je snažno suprotna psihoticizmu i sadizmu.

Big Five su međusobno slabo do umjereno povezane.

Najveće korelacije su:

Psychoticism–Sadism (0.65) Depression–Neuroticism (0.58) Extraversion-Narcissism(0.56) Machiavelism–Psychoticism (0.51)

Postoje li razlike u nekim crtama ličnosti među spolovima?

table(data_clean$sex)
## 
##            Female              Male Prefer not to say 
##               186               209                 3
df_sex <- data_clean %>%
  filter(sex %in% c("Male", "Female"))
big_five <- df_sex %>%
  pivot_longer(
    cols = c(neuroticism, extraversion, openness, agreeableness, conscientiousness),
    names_to = "trait",
    values_to = "score"
  )

ggplot(big_five, aes(x = sex, y = score, fill = sex)) +
  geom_boxplot() +
  facet_wrap(~ trait, scales = "free") +
  theme_minimal() +
  labs(
    title = "Big Five osobine po spolu (Male vs Female)",
    x = "Spol",
    y = "Rezultat"
  )

Vizualna analiza boxplotova ukazuje na obrasce razlika između spolova koji su u skladu s teorijskim očekivanjima. Najizraženije razlike uočavaju se kod neuroticizma i ugodnosti, pri čemu žene u prosjeku postižu više vrijednosti, što je vidljivo kroz više medijane i pomak distribucije prema višim vrijednostima.

Kod ekstraverzije, otvorenosti i savjesnosti razlike između spolova su manje izražene; medijani su vrlo slični, a distribucije se u velikoj mjeri preklapaju, što upućuje na izostanak izraženih spolnih razlika u tim osobinama na razini deskriptivne analize.

Prije provedbe t-testa za nezavisne uzorke, potrebno je provjeriti jesu li zadovoljene osnovne pretpostavke testa, uključujući normalnost distribucije, homogenost varijanci te nezavisnost uzoraka.

Za početak ćemo provjeriti preptpostavku o normalnosti uzorka.

ggplot(df_sex, aes(sample = neuroticism)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = agreeableness)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = openness)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = extraversion)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = conscientiousness)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

Distribucije u skupinama su priližno normalne. Zatim ćemo provjeriti varijance.

traits <- c("neuroticism", "agreeableness", "openness", "extraversion", "conscientiousness")

var_by_sex <- df_sex %>%
  group_by(sex) %>%
  summarise(across(all_of(traits), ~ var(.x, na.rm = TRUE))) 

var_by_sex
var_tests <- lapply(traits, function(tr) {
  f <- as.formula(paste(tr, "~ sex"))
  vt <- var.test(f, data = df_sex)
  tibble(
    trait = tr,
    F_statistic = round(vt$statistic, 3),
    p_value = round(vt$p.value, 4)
  )
})

bind_rows(var_tests)

Rezultati testa za jednakost varijanci pokazuju da ni za jednu od analiziranih osobina ličnosti nije utvrđena statistički značajna razlika u varijancama između muškaraca i žena. Sve dobivene p-vrijednosti veće su od 0.05, stoga se u svim slučajevima ne odbacuje nul-hipoteza o jednakosti varijanci.

Dodatno, promatramo dvije nezavisne skupine: Female i Male (ostale ćemo ukloniti).

Stoga, sve pretpostavke su zadovoljene i provest ćemo t-test za nezavisne uzorke.

# t-test za svaku osobinu
results <- lapply(traits, function(tr) {
  formula <- as.formula(paste(tr, "~ sex")) #npr. neuroticism ~ sex 
  test <- t.test(formula, data = df_sex)
  print(test$estimate)
  tibble(
    trait = tr,#naziv osobine
    t_statistic = round(test$statistic, 3), #t vrijednost
    p_value = round(test$p.value, 5),
    mean_female = round(test$estimate["mean in group Female"], 3),
    mean_male = round(test$estimate["mean in group Male"], 3)
  )
})
## mean in group Female   mean in group Male 
##           0.18251516          -0.08261147 
## mean in group Female   mean in group Male 
##            0.2738572           -0.1091680 
## mean in group Female   mean in group Male 
##           0.10694830          -0.02212707 
## mean in group Female   mean in group Male 
##          -0.14239955           0.04568951 
## mean in group Female   mean in group Male 
##           0.07941870           0.03722745
results_df <- bind_rows(results)
results_df

Rezultati dvostranih t-testova za nezavisne uzorke ukazuju na postojanje statistički značajnih spolnih razlika u pojedinim dimenzijama ličnosti. Žene postižu značajno više prosječne rezultate od muškaraca u neuroticizmu (t = 2.52, p = 0.012) i ugodnosti (t = 3.76, p < 0.001).

Za otvorenost (t = 1.22, p = 0.223), ekstraverziju (t = −1.71, p = 0.087) i savjesnost (t = 0.43, p = 0.669) nisu utvrđene statistički značajne razlike između spolova, iako su uočene blage razlike u prosječnim vrijednostima.

Sad ćemo pogledati mračne osobine.

dark_traits <- df_sex %>%
  pivot_longer(
    cols = c(narcissism, machiavelism, psychoticism, sadism),
    names_to = "trait",
    values_to = "score"
  )

ggplot(dark_traits, aes(x = sex, y = score, fill = sex)) +
  geom_boxplot() +
  facet_wrap(~ trait, scales = "free") +
  theme_minimal() +
  labs(
    title = "Mračne osobine ličnosti po spolu (Male vs Female)",
    x = "Spol",
    y = "Rezultat"
  )

Vizualna analiza mračnih osobina ličnosti ukazuje na izraženije spolne razlike u odnosu na Big Five osobine. Muškarci u prosjeku postižu više rezultate u makijavelizmu, narcizmu, psihoticizmu i sadizmu, što je vidljivo kroz više medijane i pomak distribucija prema višim vrijednostima. Razlike su posebno izražene kod sadizma i psihoticizma, dok su kod makijavelizma i narcizma prisutne umjerene razlike uz djelomično preklapanje distribucija.

Također, za mračne osobine ličnosti provest ćemo provjeru pretpostavki normalnosti distribucije i jednakosti varijanci. Analiza se temelji na istim dvjema nezavisnim skupinama ispitanik (Female i Male).

ggplot(df_sex, aes(sample = narcissism)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = machiavelism)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = psychoticism)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

ggplot(df_sex, aes(sample = sadism)) +
  stat_qq() + stat_qq_line() +
  facet_wrap(~sex)

Distribucije u skupinama su priližno normalne.

dark <- c("narcissism", "machiavelism", "psychoticism", "sadism")

var_by_sex <- df_sex %>%
  group_by(sex) %>%
  summarise(across(all_of(dark), ~ var(.x, na.rm = TRUE))) 

var_by_sex
var_tests <- lapply(dark, function(tr) {
  f <- as.formula(paste(tr, "~ sex"))
  vt <- var.test(f, data = df_sex)
  tibble(
    trait = tr,
    F_statistic = round(vt$statistic, 3),
    p_value = round(vt$p.value, 4)
  )
})

bind_rows(var_tests)

Varijance mračnih osobina ličnosti između muškaraca i žena su usporedive i približno jednake, stoga je pretpostavka homogenosti varijanci zadovoljena.

Provest ćemo t-test.

dark <- c("narcissism", "machiavelism", "psychoticism", "sadism")

dark_results <- lapply(dark, function(tr) {
  formula <- as.formula(paste(tr, "~ sex"))
  test <- t.test(formula, data = df_sex)
  tibble(
    trait = tr,
    t_statistic = round(test$statistic, 3),
    p_value = round(test$p.value, 5),
    mean_female = round(test$estimate["mean in group Female"], 3),
    mean_male = round(test$estimate["mean in group Male"], 3)
  )
})

dark_results_df <- bind_rows(dark_results)
dark_results_df

U analizi mračnih osobina ličnosti pronađene su jasne spolne razlike. Budući da je u t-testu korišten format tr ~ sex, negativne t-vrijednosti ukazuju na više rezultate u skupini muškaraca u odnosu na žene.

Rezultati pokazuju da muškarci postižu statistički značajno više rezultate na svim analiziranim mračnim crtama — narcizmu, makijavelizmu, psihoticizmu i sadizmu (sve p < 0.05). Najizraženija razlika uočena je kod sadizma, gdje muškarci ostvaruju znatno više prosječne vrijednosti u odnosu na žene, što upućuje na izraženije spolne razlike u ovoj dimenziji ličnosti.

df_sex$sex <- factor(df_sex$sex, levels = c("Female", "Male"))
levels(df_sex$sex)
## [1] "Female" "Male"
traits_dark <- c("narcissism", "machiavelism", 
                 "psychoticism", "sadism")

results_one_tailed <- lapply(traits_dark, function(tr) {
  f <- as.formula(paste(tr, "~ sex"))
  test <- t.test(f, data = df_sex, alternative = "less")
  
  tibble(
    trait = tr,
    t_statistic = round(test$statistic, 3),
    p_value = round(test$p.value, 5),
    mean_female = round(test$estimate["mean in group Female"], 3),
    mean_male = round(test$estimate["mean in group Male"], 3)
  )
})

results_one_tailed_df <- bind_rows(results_one_tailed)
results_one_tailed_df

Rezultati jednostranog t-testa, provedenog u smjeru teorijske pretpostavke da muškarci postižu više rezultate od žena, potvrđuju postojanje statistički značajnih spolnih razlika u svim analiziranim mračnim osobinama ličnosti. Muškarci ostvaruju značajno više vrijednosti u narcizmu, makijavelizmu, psihoticizmu i sadizmu, pri čemu je razlika najizraženija kod sadizma.

Jačaju li neke osobine s godinama?

Nezavisna varijabla (prediktori):

–>Dob (age)

Zavisne varijable:

–> Ekstraverzija (extraversion) –> Ugodnost (agreeableness) –> Savjesnost (conscientiousness) –> Neuroticizam (neuroticism) –> Otvorenost (openness)

U nastavku se analiza provodi zasebno za svaku osobinu. Budući da su i dob i crte ličnosti kontinuirane varijable, a istraživačko pitanje se odnosi na linearnu promjenu s godinama, jednostavna linearna regresija predstavlja najprikladniji statistički pristup.

describe(data_clean %>%
  select(age, extraversion, agreeableness,
         conscientiousness, neuroticism, openness))

Deskriptivna statistika pruža osnovni uvid u raspodjelu dobi i razinu pojedinih crta ličnosti u uzorku ispitanika.

ggplot(data_clean, aes(age)) +
  geom_histogram(bins = 30, fill = "steelblue") +
  theme_minimal()

Histogram dobi prikazuje raspodjelu ispitanika po dobnim skupinama te omogućuje procjenu raspona i strukture dobi u uzorku.

ggplot(data_clean, aes(age, extraversion)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

ggplot(data_clean, aes(age, agreeableness)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

ggplot(data_clean, aes(age, conscientiousness)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

ggplot(data_clean, aes(age, neuroticism)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

ggplot(data_clean, aes(age, openness)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

Raspršeni dijagrami s pripadajućim regresijskim linijama korišteni su za vizualnu procjenu linearnog odnosa između dobi i pojedinih crta ličnosti. Grafički prikazi ne upućuju na izražene linearne trendove, iako se kod nekih osobina može uočiti blagi rast ili pad vrijednosti s porastom dobi.

cor.test(data_clean$age, data_clean$extraversion)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$age and data_clean$extraversion
## t = -1.7053, df = 396, p-value = 0.08893
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.18215014  0.01302653
## sample estimates:
##         cor 
## -0.08538084
cor.test(data_clean$age, data_clean$agreeableness)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$age and data_clean$agreeableness
## t = 1.2789, df = 396, p-value = 0.2017
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.0343782  0.1614170
## sample estimates:
##        cor 
## 0.06413658
cor.test(data_clean$age, data_clean$conscientiousness)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$age and data_clean$conscientiousness
## t = -0.13972, df = 396, p-value = 0.889
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.10524642  0.09134006
## sample estimates:
##          cor 
## -0.007021018
cor.test(data_clean$age, data_clean$neuroticism)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$age and data_clean$neuroticism
## t = 0.2454, df = 396, p-value = 0.8063
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.08607148  0.11049500
## sample estimates:
##        cor 
## 0.01233089
cor.test(data_clean$age, data_clean$openness)
## 
##  Pearson's product-moment correlation
## 
## data:  data_clean$age and data_clean$openness
## t = -0.69464, df = 396, p-value = 0.4877
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.13272862  0.06363051
## sample estimates:
##         cor 
## -0.03488574

Pearsonove korelacije korištene su kao preliminarna analiza odnosa dobi i crta ličnosti. Rezultati korelacija ne upućuju na statistički značajne povezanosti između dobi i promatranih osobina.

vars <- data_clean %>%
  select(age, extraversion, agreeableness,
         conscientiousness, neuroticism, openness) %>%
  na.omit()

corrplot(cor(vars))

Korelacijska matrica dodatno potvrđuje izostanak snažnih povezanosti između dobi i pojedinih crta ličnosti.

model_consc <- lm(conscientiousness ~ age, data = data_clean)
summary(model_consc)
## 
## Call:
## lm(formula = conscientiousness ~ age, data = data_clean)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.99434 -0.68117  0.01346  0.76485  2.34600 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.099902   0.353798   0.282    0.778
## age         -0.001533   0.010973  -0.140    0.889
## 
## Residual standard error: 0.9919 on 396 degrees of freedom
## Multiple R-squared:  4.929e-05,  Adjusted R-squared:  -0.002476 
## F-statistic: 0.01952 on 1 and 396 DF,  p-value: 0.889
model_extra <- lm(extraversion ~ age, data = data_clean)
summary(model_extra)
## 
## Call:
## lm(formula = extraversion ~ age, data = data_clean)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1645 -0.6666  0.1027  0.7857  2.5834 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.61250    0.38726   1.582   0.1145  
## age         -0.02048    0.01201  -1.705   0.0889 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.086 on 396 degrees of freedom
## Multiple R-squared:  0.00729,    Adjusted R-squared:  0.004783 
## F-statistic: 2.908 on 1 and 396 DF,  p-value: 0.08893
model_agree <- lm(agreeableness ~ age, data = data_clean)
summary(model_agree)
## 
## Call:
## lm(formula = agreeableness ~ age, data = data_clean)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1780 -0.7163  0.0236  0.7345  2.6385 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.39279    0.36742  -1.069    0.286
## age          0.01457    0.01140   1.279    0.202
## 
## Residual standard error: 1.03 on 396 degrees of freedom
## Multiple R-squared:  0.004114,   Adjusted R-squared:  0.001599 
## F-statistic: 1.636 on 1 and 396 DF,  p-value: 0.2017
model_neuro <- lm(neuroticism ~ age, data = data_clean)
summary(model_neuro)
## 
## Call:
## lm(formula = neuroticism ~ age, data = data_clean)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3342 -0.7428 -0.1191  0.6403  2.9115 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.045980   0.376568  -0.122    0.903
## age          0.002866   0.011679   0.245    0.806
## 
## Residual standard error: 1.056 on 396 degrees of freedom
## Multiple R-squared:  0.0001521,  Adjusted R-squared:  -0.002373 
## F-statistic: 0.06022 on 1 and 396 DF,  p-value: 0.8063
model_open <- lm(openness ~ age, data = data_clean)
summary(model_open)
## 
## Call:
## lm(formula = openness ~ age, data = data_clean)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4319 -0.6082 -0.1301  0.6922  2.9697 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.297455   0.373452   0.796    0.426
## age         -0.008046   0.011583  -0.695    0.488
## 
## Residual standard error: 1.047 on 396 degrees of freedom
## Multiple R-squared:  0.001217,   Adjusted R-squared:  -0.001305 
## F-statistic: 0.4825 on 1 and 396 DF,  p-value: 0.4877

Za svaku crtu ličnosti provedena je analiza jednostavne linearne regresije u kojoj je dob korištena kao nezavisna varijabla. U niti jednom modelu dob se nije pokazala statistički značajnim prediktorom (p > 0.05). Vrijednosti koeficijenta determinacije bile su vrlo niske, što upućuje na slab objašnjavajući doprinos dobi.

Na temelju provedene analize može se zaključiti da se u promatranom uzorku ne uočava statistički značajno jačanje niti slabljenje crta ličnosti s godinama. Dob se u ovom istraživanju nije pokazala značajnim prediktorom promjena u okviru Big Five modela ličnosti.

library(broom)

models <- list(
  Extraversion = model_extra,
  Agreeableness = model_agree,
  Conscientiousness = model_consc,
  Neuroticism = model_neuro,
  Openness = model_open
)

results <- lapply(models, tidy) |> 
  bind_rows(.id = "Trait") |> 
  filter(term == "age")

results

Tablica prikazuje procijenjene regresijske koeficijente za učinak dobi na pojedine crte ličnosti.

Jesu li crte ličnosti i sklonost stresu, depresiji i anksioznosti povezane sa zanimanjem?

df_job <- dataset %>% filter(!sex %in% c("CONSENT_REVOKED"),
                             !`student status` %in% c("CONSENT_REVOKED", "DATA_EXPIRED"),
                             !`employment status` %in% c("CONSENT_REVOKED", "DATA_EXPIRED")
                             )
df_job <- df_job %>% mutate(
    occupation_group = if_else(
      `student status` == "Yes",
      "Student",
      `employment status`
    )
  ) %>% filter(!occupation_group %in% c("Other", "Due to start a new job within the next month", "Not in paid work (e.g. homemaker', 'retired or disabled)"))

table(df_job$occupation_group)
## 
##                    Full-Time                    Part-Time 
##                          205                           36 
##                      Student Unemployed (and job seeking) 
##                          109                           24
df_job %>%
  group_by(occupation_group) %>%
  summarise(
    n = n(),
    mean_stress = mean(stress, na.rm = TRUE),
    mean_depression = mean(depression, na.rm = TRUE),
    mean_anxiety = mean(anxiety, na.rm = TRUE)
  )
mental_long <- df_job %>%
  pivot_longer(
    cols = c(stress, depression, anxiety),
    names_to = "outcome",
    values_to = "score"
  )

ggplot(mental_long, aes(x = occupation_group, y = score, fill = occupation_group)) +
  geom_boxplot() +
  facet_wrap(~ outcome, scales = "free_y") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
  labs(
    title = "Stres, depresija i anksioznost po zanimanju",
    x = "Zanimanje",
    y = "Rezultat"
  )

Vizualni pregled distribucija pokazuje da se razine stresa, depresije i anksioznosti uvelike preklapaju između skupina definiranih prema zanimanju, što upućuje na izražene individualne razlike unutar skupina. Iako nezaposleni sudionici pokazuju viši medijan depresivnosti u odnosu na ostale skupine, razlike nisu statistički potvrđene. Razine stresa pokazuju vrlo slične obrasce u svim skupinama, dok se anksioznost nepojavljuje sustavno povezanom sa zanimanjem. Ovi nalazi sugeriraju da profesionalni status sam po sebi ima ograničen doprinos objašnjenju mentalnog zdravlja te da individualne crte ličnosti vjerojatno imaju snažniju ulogu.

Provođenje ANOVA analize - Razlikuju li se razine anksioznosti, depresije i stresa po zanimanjima?

Test pretpostavke normalnosti za anksioznost

require(nortest)
lillie.test(df_job$anxiety)
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety
## D = 0.040688, p-value = 0.1385
lillie.test(df_job$anxiety[df_job$occupation_group=='Full-Time'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Full-Time"]
## D = 0.060222, p-value = 0.06789
lillie.test(df_job$anxiety[df_job$occupation_group=='Part-Time'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Part-Time"]
## D = 0.15146, p-value = 0.03593
lillie.test(df_job$anxiety[df_job$occupation_group=='Unemployed (and job seeking)'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Unemployed (and job seeking)"]
## D = 0.11293, p-value = 0.5953
lillie.test(df_job$anxiety[df_job$occupation_group=='Student'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Student"]
## D = 0.042081, p-value = 0.9066
hist(df_job$anxiety[df_job$occupation_group=='Full-Time'])

hist(df_job$anxiety[df_job$occupation_group=='Part-Time'])

hist(df_job$anxiety[df_job$occupation_group=='Unemployed (and job seeking)'])

hist(df_job$anxiety[df_job$occupation_group=='Student'])

Test pretpostavke normalnosti za depresiju

require(nortest)
lillie.test(df_job$anxiety)
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety
## D = 0.040688, p-value = 0.1385
lillie.test(df_job$anxiety[df_job$occupation_group=='Full-Time'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Full-Time"]
## D = 0.060222, p-value = 0.06789
lillie.test(df_job$anxiety[df_job$occupation_group=='Part-Time'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Part-Time"]
## D = 0.15146, p-value = 0.03593
lillie.test(df_job$anxiety[df_job$occupation_group=='Unemployed (and job seeking)'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Unemployed (and job seeking)"]
## D = 0.11293, p-value = 0.5953
lillie.test(df_job$anxiety[df_job$occupation_group=='Student'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$anxiety[df_job$occupation_group == "Student"]
## D = 0.042081, p-value = 0.9066
hist(df_job$anxiety[df_job$occupation_group=='Full-Time'])

hist(df_job$anxiety[df_job$occupation_group=='Part-Time'])

hist(df_job$anxiety[df_job$occupation_group=='Unemployed (and job seeking)'])

hist(df_job$anxiety[df_job$occupation_group=='Student'])

Test pretpostavki normalnosti za stres

require(nortest)
lillie.test(df_job$stress)
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$stress
## D = 0.038095, p-value = 0.2075
lillie.test(df_job$stress[df_job$occupation_group=='Full-Time'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$stress[df_job$occupation_group == "Full-Time"]
## D = 0.057729, p-value = 0.09354
lillie.test(df_job$stress[df_job$occupation_group=='Part-Time'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$stress[df_job$occupation_group == "Part-Time"]
## D = 0.091433, p-value = 0.6263
lillie.test(df_job$stress[df_job$occupation_group=='Unemployed (and job seeking)'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$stress[df_job$occupation_group == "Unemployed (and job seeking)"]
## D = 0.070023, p-value = 0.9916
lillie.test(df_job$stress[df_job$occupation_group=='Student'])
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  df_job$stress[df_job$occupation_group == "Student"]
## D = 0.062087, p-value = 0.3808
hist(df_job$stress[df_job$occupation_group=='Full-Time'])

hist(df_job$stress[df_job$occupation_group=='Part-Time'])

hist(df_job$stress[df_job$occupation_group=='Unemployed (and job seeking)'])

hist(df_job$stress[df_job$occupation_group=='Student'])

Test pretpostavki homogenosti varijanci za anksioznost

bartlett.test(df_job$anxiety ~ df_job$occupation_group)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  df_job$anxiety by df_job$occupation_group
## Bartlett's K-squared = 1.0818, df = 3, p-value = 0.7815
var((df_job$anxiety[df_job$occupation_group=='Full-Time']))
## [1] 0.9497347
var((df_job$anxiety[df_job$occupation_group=='Part-Time']))
## [1] 1.159903
var((df_job$anxiety[df_job$occupation_group=='Unemployed (and job seeking)']))
## [1] 1.070241
var((df_job$anxiety[df_job$occupation_group=='Student']))
## [1] 1.091825

Test pretpostavki homogenosti varijanci za depresiju

bartlett.test(df_job$depression ~ df_job$occupation_group)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  df_job$depression by df_job$occupation_group
## Bartlett's K-squared = 0.78061, df = 3, p-value = 0.8541
var((df_job$depression[df_job$occupation_group=='Full-Time']))
## [1] 1.200926
var((df_job$depression[df_job$occupation_group=='Part-Time']))
## [1] 1.220683
var((df_job$depression[df_job$occupation_group=='Unemployed (and job seeking)']))
## [1] 0.9148913
var((df_job$depression[df_job$occupation_group=='Student']))
## [1] 1.222059

Test pretpostavki homogenosti varijanci za stres

bartlett.test(df_job$stress ~ df_job$occupation_group)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  df_job$stress by df_job$occupation_group
## Bartlett's K-squared = 3.3471, df = 3, p-value = 0.3411
var((df_job$stress[df_job$occupation_group=='Full-Time']))
## [1] 1.14987
var((df_job$stress[df_job$occupation_group=='Part-Time']))
## [1] 0.8855903
var((df_job$stress[df_job$occupation_group=='Unemployed (and job seeking)']))
## [1] 1.022324
var((df_job$stress[df_job$occupation_group=='Student']))
## [1] 1.408198
summary(aov(anxiety ~ occupation_group, data = df_job))
##                   Df Sum Sq Mean Sq F value Pr(>F)
## occupation_group   3    4.0   1.339   1.314  0.269
## Residuals        370  376.9   1.019
summary(aov(depression ~ occupation_group, data = df_job))
##                   Df Sum Sq Mean Sq F value Pr(>F)  
## occupation_group   3    8.3   2.781   2.334 0.0736 .
## Residuals        370  440.7   1.191                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(stress ~ occupation_group, data = df_job))
##                   Df Sum Sq Mean Sq F value Pr(>F)
## occupation_group   3    2.2   0.732   0.614  0.606
## Residuals        370  441.2   1.192

Provedene su jednosmjerne analize varijance (ANOVA) s ciljem ispitivanja razlika u razini anksioznosti, depresije i stresa između skupina definiranih prema zanimanju. Prethodno tome, provedena su testiranja pretpostavki normalnosti podataka i homogenosti varijanci za anksioznost, depresiju i stres s obzirom na kategoriju koja opisuje radni odnos occupation_group. Sve su se pretpostavke pokazale ispravnima.

Provedene su jednosmjerne analize varijance (ANOVA) s ciljem ispitivanja razlika u razini anksioznosti, depresije i stresa između skupina definiranih prema zanimanju.

Rezultati pokazuju da ne postoje statistički značajne razlike u razini anksioznosti među zanimanjima, F(3, 370) = 1.31, p = 0.269. Također, nisu utvrđene statistički značajne razlike u razini stresa, F(3, 370) = 0.61, p = 0.606.

Za depresiju je uočen trend prema razlikama između skupina, no rezultat nije dosegnuo konvencionalnu razinu statističke značajnosti, F(3, 370) = 2.33, p = 0.0736. Dobiveni nalazi upućuju na to da zanimanje samo po sebi nije snažan prediktor razine mentalnog zdravlja u ovom uzorku.

Provođenje višestruke regresije za pokazivanje doprinosa zanimanja anksioznosti povrh ličnosti

model_anxiety <- lm(
  anxiety ~ occupation_group + 
  narcissism + machiavelism + psychoticism + sadism + neuroticism +
  extraversion + openness + agreeableness + conscientiousness,
  data = df_job
)

summary(model_anxiety)
## 
## Call:
## lm(formula = anxiety ~ occupation_group + narcissism + machiavelism + 
##     psychoticism + sadism + neuroticism + extraversion + openness + 
##     agreeableness + conscientiousness, data = df_job)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8777 -0.5030  0.0377  0.5391  3.2731 
## 
## Coefficients:
##                                               Estimate Std. Error t value
## (Intercept)                                   0.010784   0.064791   0.166
## occupation_groupPart-Time                     0.171681   0.168508   1.019
## occupation_groupStudent                      -0.110070   0.110430  -0.997
## occupation_groupUnemployed (and job seeking)  0.048740   0.210452   0.232
## narcissism                                   -0.066293   0.063274  -1.048
## machiavelism                                  0.089268   0.058164   1.535
## psychoticism                                  0.069755   0.068022   1.025
## sadism                                        0.070111   0.063485   1.104
## neuroticism                                   0.372737   0.064679   5.763
## extraversion                                  0.117466   0.068659   1.711
## openness                                      0.066920   0.050444   1.327
## agreeableness                                -0.035415   0.064335  -0.550
## conscientiousness                            -0.007022   0.064727  -0.108
##                                              Pr(>|t|)    
## (Intercept)                                     0.868    
## occupation_groupPart-Time                       0.309    
## occupation_groupStudent                         0.320    
## occupation_groupUnemployed (and job seeking)    0.817    
## narcissism                                      0.295    
## machiavelism                                    0.126    
## psychoticism                                    0.306    
## sadism                                          0.270    
## neuroticism                                  1.77e-08 ***
## extraversion                                    0.088 .  
## openness                                        0.185    
## agreeableness                                   0.582    
## conscientiousness                               0.914    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9153 on 361 degrees of freedom
## Multiple R-squared:  0.2061, Adjusted R-squared:  0.1797 
## F-statistic: 7.807 on 12 and 361 DF,  p-value: 5.873e-13

U svrhu ispitivanja odnosa između zanimanja i anksioznosti, proveden je model višestruke linearne regresije kojim se ispituje doprinos radnog statusa povrh crta ličnosti.

Rezultati pokazuju da je model statistički značajan u cjelini (F(12, 361) = 7.807, p = 5.873x\(10^{-13}\)), pri čemu Multiple R-squared iznosi 0.2061, a Adjusted R-squared 0.1797. Iako je objašnjeni udio varijance manji u odnosu na modele za stres i depresiju, vrijednosti upućuju na to da model ipak ima smisla za interpretaciju.

Analizom mračnih crta ličnosti nije utvrđen nijedan statistički značajan prediktor anksioznosti. Narcizam, makijavelizam, psihoticizam i sadizam nisu pokazali jedinstveni doprinos u ovom modelu, što sugerira da se njihova povezanost s anksioznošću ne zadržava nakon uključivanja ostalih crta ličnosti.

Unutar petofaktorskog modela ličnosti, neuroticizam se jasno istaknuo kao ključni prediktor anksioznosti (\(\beta\) = 0.372737, p = 1.77x\(10^{-8}\)). Osobe s višim razinama neuroticizma pokazuju izraženiju anksioznost, neovisno o zanimanju i ostalim osobinama ličnosti, što je u skladu s postojećim teorijskim i empirijskim nalazima. Ekstraverzija nije dosegnula razinu statističke značajnosti (\(\beta\) = 0.117466, p = 0.088), no uočen je slab trend koji upućuje na višu razinu anksioznosti kod ekstravertiranijih osoba. Ostale Big Five crte nisu se pokazale značajnima u ovom modelu.

Provođenje višestruke regresije za pokazivanje doprinosa zanimanja depresiji povrh ličnosti

model_depression <- lm(
  depression ~ occupation_group + 
  narcissism + machiavelism + psychoticism + sadism + neuroticism +
  extraversion + openness + agreeableness + conscientiousness,
  data = df_job
)

summary(model_depression)
## 
## Call:
## lm(formula = depression ~ occupation_group + narcissism + machiavelism + 
##     psychoticism + sadism + neuroticism + extraversion + openness + 
##     agreeableness + conscientiousness, data = df_job)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.02110 -0.46296  0.03503  0.47615  2.57324 
## 
## Coefficients:
##                                               Estimate Std. Error t value
## (Intercept)                                   0.056563   0.057575   0.982
## occupation_groupPart-Time                    -0.002998   0.149741  -0.020
## occupation_groupStudent                      -0.035153   0.098132  -0.358
## occupation_groupUnemployed (and job seeking) -0.181134   0.187013  -0.969
## narcissism                                   -0.027405   0.056227  -0.487
## machiavelism                                  0.088226   0.051687   1.707
## psychoticism                                  0.129060   0.060446   2.135
## sadism                                        0.015564   0.056414   0.276
## neuroticism                                   0.439192   0.057476   7.641
## extraversion                                 -0.302426   0.061012  -4.957
## openness                                      0.031826   0.044826   0.710
## agreeableness                                 0.056346   0.057170   0.986
## conscientiousness                            -0.018329   0.057518  -0.319
##                                              Pr(>|t|)    
## (Intercept)                                    0.3266    
## occupation_groupPart-Time                      0.9840    
## occupation_groupStudent                        0.7204    
## occupation_groupUnemployed (and job seeking)   0.3334    
## narcissism                                     0.6263    
## machiavelism                                   0.0887 .  
## psychoticism                                   0.0334 *  
## sadism                                         0.7828    
## neuroticism                                  1.96e-13 ***
## extraversion                                 1.10e-06 ***
## openness                                       0.4782    
## agreeableness                                  0.3250    
## conscientiousness                              0.7502    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8133 on 361 degrees of freedom
## Multiple R-squared:  0.4682, Adjusted R-squared:  0.4506 
## F-statistic: 26.49 on 12 and 361 DF,  p-value: < 2.2e-16

Kako bi se ispitao doprinos zanimanja depresiji uz kontrolu crta ličnosti, proveden je model višestruke linearne regresije.

Model se pokazao izrazito snažnim u objašnjenju ishoda, s vrijednostima F(12, 361) = 26.49 i p = 2.2x\(10^{-16}\). Multiple R-squared iznosi 0.4682, dok Adjusted R-squared iznosi 0.4506, što upućuje na to da model objašnjava velik dio varijance depresije te ima vrlo dobru objašnjavajuću snagu.

Među mračnim crtama ličnosti, psihoticizam se ponovno pokazao statistički značajnim pozitivnim prediktorom depresije (\(\beta\) = 0.204240, p = 0.00316). Ovaj rezultat sugerira da osobe s izraženijim obilježjima psihoticizma imaju višu razinu depresije, čak i nakon kontrole ostalih osobina ličnosti i radnog statusa. Makijavelizam je pokazao granični efekt (\(\beta\) = 0.112090, p = 0.05728), dok narcizam i sadizam nisu imali značajan doprinos u objašnjenju depresije.

Unutar petofaktorskog modela, neuroticizam se ponovno istaknuo kao najsnažniji pozitivni prediktor depresije (\(\beta\) = 0.439192, p = 1.96x\(10^{-13}\)), potvrđujući njegovu ključnu ulogu u objašnjenju emocionalnih poteškoća. Za razliku od modela za stres i anksioznost, ekstraverzija se ovdje pokazala statistički značajnim negativnim prediktorom (\(\beta\) = -0.302426, p = 1.10x\(10^{-6}\)), što upućuje na to da osobe s višom razinom ekstraverzije pokazuju nižu razinu depresije. Ostale crte Big Five modela nisu se pokazale značajnima.

Provođenje višestruke regresije za pokazivanje doprinosa zanimanja depresiji povrh ličnosti

model_stress <- lm(
  stress ~ occupation_group + 
  narcissism + machiavelism + psychoticism + sadism + neuroticism +
  extraversion + openness + agreeableness + conscientiousness,
  data = df_job
)

summary(model_stress)
## 
## Call:
## lm(formula = stress ~ occupation_group + narcissism + machiavelism + 
##     psychoticism + sadism + neuroticism + extraversion + openness + 
##     agreeableness + conscientiousness, data = df_job)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0898 -0.5186  0.0879  0.5882  3.2164 
## 
## Coefficients:
##                                               Estimate Std. Error t value
## (Intercept)                                   0.006104   0.065465   0.093
## occupation_groupPart-Time                     0.089980   0.170263   0.528
## occupation_groupStudent                       0.046961   0.111580   0.421
## occupation_groupUnemployed (and job seeking) -0.362641   0.212643  -1.705
## narcissism                                   -0.012195   0.063933  -0.191
## machiavelism                                  0.112090   0.058770   1.907
## psychoticism                                  0.204240   0.068730   2.972
## sadism                                       -0.029011   0.064146  -0.452
## neuroticism                                   0.406136   0.065353   6.215
## extraversion                                 -0.084191   0.069374  -1.214
## openness                                      0.142228   0.050970   2.790
## agreeableness                                -0.048592   0.065005  -0.748
## conscientiousness                             0.004554   0.065401   0.070
##                                              Pr(>|t|)    
## (Intercept)                                   0.92576    
## occupation_groupPart-Time                     0.59749    
## occupation_groupStudent                       0.67410    
## occupation_groupUnemployed (and job seeking)  0.08898 .  
## narcissism                                    0.84883    
## machiavelism                                  0.05728 .  
## psychoticism                                  0.00316 ** 
## sadism                                        0.65135    
## neuroticism                                  1.42e-09 ***
## extraversion                                  0.22570    
## openness                                      0.00554 ** 
## agreeableness                                 0.45525    
## conscientiousness                             0.94453    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9248 on 361 degrees of freedom
## Multiple R-squared:  0.3036, Adjusted R-squared:  0.2805 
## F-statistic: 13.12 on 12 and 361 DF,  p-value: < 2.2e-16

Iz modela višestruke linearne regresije koji izračunava doprinos zanimanja stresu povrh ličnosti zaključujemo sljedeće stvari.

Model se pokazuje statistički značajnim u cjelini s vrijednostima F(12, 361) = 13.12 i p = 2.2x\(10^{-16}\) (< 0.001) te je Multiple R-squared = 0.3036 i Adjusted R-squared = 0.2805. Ove vrijednosti upućuju da model ima dobru potpornu (objašnjavajuću) snagu.

Među mračnim crtama ličnosti, psihoticizam se istaknuo kao statistički značajan pozitivan prediktor (\(\beta\) = 0.204240, p = 0.00316 (< 0.01)). To znači da osobe s višim razinama psihoticizma pokazuju višu razinu stresa, čak i nakon utjecaja ostalih crta ličnosti i oblika radnog angažmana. Makijavelizam je pokazao trend prema pozitivnoj povezanosti (\(/beta\) = 0.112090, p = 0.05728 (< 0.1)), ali rezultati su nedovoljni za snažnu povezanost. Narcizam i sadizam nisu pokazali značajan doprinos.

Unutar petofaktorskog Big 5 modela, neurocitizam se pokazao daleko najsnažnijim prediktorom ishoda (\(\beta\) = 0.406136, p = 1.42x\(10^{-9}\) (< 0.001)). Viša razina neurocitizma povezana je s višom razinom stresa, neovisno o radnom odnosu i ostalim crtama ličnosti. Ovaj rezultat je u potpunosti u skladu s teorijskim očekivanjima. Izdvajamo i otvorenost kao statistički značajan pozititvan prediktor (\(\beta\) = 0.142228, p = 0.00554 (< 0.01). Ovaj podatak sugerira da osobe s više otvorenosti mogu biti osjetljivije na stres. Ekstraverzija, ugodnost i savjesnost nisu pokazale statistički značajan u ovom modelu.